Name: Varenne

Who is asking: Student Level: Secondary

Question:
I am having SO much trouble tackling this question and don't know what the right answer is... can you help me out? The question is

Find the equation of the normal to the curve y=(x-2)2/(1-x)2 that is parallel to the line x+4y+7=0

Hi Varenne,

If a nornal to curve is parallel to x+4y+7 = 0 then these two lines have the same slope. If you write x+4y+7 = 0 as

y = -1/4 x - 7/4 You see that its slope is  -1/4. Thus the normal you are looking for has slope  -1/4.

Since the normal line at a point is perpendicular to the tangent line at that point, the slope of the tangent line is 4. What remains is to differentiate the function, set the derivative equal to 4 and solve for x. Finally write the equation of the line through each such point with slope -1/4

Cheers,
Harley
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